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Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.

The analysis of stride series revealed a loss of complexity in older people, which correlated with the falling propensity. A recent experiment evidenced an increase of walking complexity in older participants when they walked in close synchrony with a younger companion. Moreover, a prolonged experience of such synchronized walking yielded a persistent restoration of complexity. This result, however, was obtained with a unique healthy partner, and it could be related to a particular partner’s behavior. The authors’ aim was to replicate this important finding using a different healthy partner and to compare the results to those previously obtained. The authors successfully replicated the previous results: synchronization yielded an attraction of participants’ complexity toward that of their partner and a restoration of complexity that persisted in two posttests, 2 and 6 weeks after the end of the training sessions. This study shows that this complexity restoration protocol can be applied successfully with another partner, and allows us to conclude that it can be generalized.

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